Images are only shown if users are accessing their email using a client (e.g. their web browser) that shares the same session that they have used to log into JIRA. In the case that they are not, no image is shown.

Steps to reproduce:

1. Go to user1's User Profile and choose a 'Custom Image' through the Avatar picker.
2. Perform an activity that notifies user2 via email (e.g. @mention).
3. Ensure that you are not logged into JIRA and check user2's email inbox.
4. BUG: Custom image picked by user1 is not shown in email notifications.

Special note: This has reoccured in later versions of JIRA and is being worked on in JRA-41675.